COH Periodic Wave Oscillators

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From the Update 11/11/2010: The strongest frequency, according to classical frequency analysis, is an oscillation with a length of 10 trading sessions.

Frequency Analysis based on Monthly Comb

COH:  Frequency Analysis based on Monthly Comb

It is obvious from inspection of price lines, that many seem to contain cycles that may persist in repeating for a long time. Through the years, technicians have expended much effort to measure and exploit these cycles. It would appear simple enough to do a frequency analysis on the time series. But the cycles or periods that seem so easy to see in the price data, have proven to be surprisingly difficult to measure by classical methods. The classical methods apply to stationary cycles of exactly regular period. We can easily remove the trends from historical price data to make the series stationary. However, the fluctuations seen in financial data are almost never exactly periodic, a fact that has played havoc with most schemes to exploit the market cycles.

One factor in the behaviour of market fluctuations is "Anticipation". When speculators detect a cycle in prices, they will buy earlier before the peak, and sell earlier before the dip. This phenomena causes an increase in frequency, and eventually a breakup of the established cycle. Traditional frequency analysis methods such as the Fourier Transform, break down badly attempting to deal with these irregularities.

Wilder estimated that there was an important period of about 28 trading sessions. The half cycle of this period (14 sessions) is a default factor in many of the technical indicators. We have found this to be a reasonable figure, even in today's markets, but there is significant variation between issues. Some companies just seem to have faster or slower cycles for one reason or another, and the indicators may be more accurate when fitted to the situation.

The paradoxical condition of variable length periods forces the adoptation of some new forms of analysis.




General Market Conditions

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Frequency from Monthly Comb Filter
Representative Cycle (Trading Sessions) = 36.00
Sawtooth = 45.06
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High16.2333.0036.0013.66 %
Low16.6731.0028.0013.17 %
Recent HighPriceRecent LowPrice Cycle
Monday, August 30, 201035.6330
Wednesday, August 04, 201039.1435
Monday, July 19, 201034.2340
Tuesday, June 15, 201044.1436
Thursday, May 20, 201037.5282
Friday, April 23, 201043.2932
Tuesday, March 09, 201038.5738
Friday, January 22, 201033.7141


Fourier Transform after Digital Filter M

Cycle LengthFourier Amplitude
130.46
160.29
210.28
240.27
370.19
260.17
430.17
330.17
390.13
280.13
510.13



Frequency Analysis based on Quarterly Comb

Frequency Analysis based on Quarterly Comb of Coach, Inc.

Frequency from Quarterly Comb Filter
Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 49.86
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High46.7591.000.0017.67 %
Low51.2581.000.0021.25 %
Recent HighPriceRecent LowPrice Cycle
Monday, July 19, 201034.23122
Tuesday, June 15, 201044.1436
Friday, April 23, 201043.2970
Friday, January 22, 201033.71135
Tuesday, January 12, 201038.23156
Friday, July 10, 200923.2286
Monday, June 01, 200927.88112
Monday, March 09, 200911.5372


Fourier Transform after Digital Filter Q

Cycle LengthFourier Amplitude
100.26
120.24
1370.21
150.16
210.16
170.16
850.15
3410.15
1080.15
240.15
790.14



Frequency Analysis based on Yearly Comb

COH:  Frequency Analysis based on Yearly Comb

Representative Cycle (Trading Sessions) = 0.00
Sawtooth = 44.19
Peak TypeAvg. CycleMedian CycleCycle ModeCycle Amplitude
High0.000.000.000.00 %
Low0.000.000.000.00 %
Recent HighPriceRecent LowPrice Cycle
Monday, March 09, 200911.53288
Thursday, May 15, 200836.81270
Tuesday, January 15, 200824.20376
Friday, April 20, 200752.88277
Tuesday, July 18, 200625.15489
Tuesday, March 14, 200636.341169
Monday, August 09, 200417.75515
Tuesday, July 17, 20015.19196


Fourier Transform on Raw Closing Prices

Cycle LengthFourier Amplitude
6838.18
4103.96
5123.06
2932.81
2561.86
1861.56
2281.37
1461.29
141.22
201.18
1581.15




Breaking News:

In the news, Monday, November 15, 2010: A favorable condition has developed with Sprint Nextel Corporation, ticker symbol S. Also, there are breaking events concerning Abbott Laboratories (ABT) and Cree, Inc. (CREE)


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COH




Coach, Inc.












Average Sawtooth based on Monthly Combo

Average Sawtooth based on Monthly Combo of Coach, Inc.

COH




Coach, Inc.









Average Sawtooth based on Bi-weekly Combo

Average Sawtooth based on Bi-weeklyly Combo of Coach, Inc.



A comparison of the average distance (in time) from each periodic high to to next periodic low, against the distance to the following high point, yields the Sawtooth Statistic. The mid-point, corresponding to a perfect sine wave, is 50 percent. Values less than this indicate the sell slope is steeper than the buy slope, while values over 50 percent show the opposite.

The Sawtooth Statistic gives a clue to the general mood of the markets, functioning as a sort of sentiment indicator. The chart represents the sawtooth percentage of (approximately) monthly cycles over the past year, and of the (approximately) bi-weekly cycles, averaged over the past six months.




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